Robust adaptive regulation of discrete time nonlinear systems with arbitrary nonlinearities

The Hammerstein-Wiener model is a block-oriented model, having a linear dynamic block sandwiched by two static nonlinear blocks. This note develops an adaptive controller for a special form of Hammerstein-Wiener nonlinear systems which are parameterized by the key-term separation principle. The adaptive control law and recursive parameter estimation are updated by the use of internal variable estimations. By modeling the errors due to the estimation of internal variables, we establish convergence and stability properties. Theoretical results show that parameter estimation convergence and closed-loop system stability can be guaranteed under sufficient condition. From a qualitative analysis of the sufficient condition, we introduce an adaptive weighted factor to improve the performance of the adaptive controller. Numerical examples are given to confirm the results in this paper.

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“…Proof of Lemma 1: The proof of this lemma is motivated by Boutayeb and Darouach (1995) and Fu and Chai (2013).…”

Section: Convergence Propertiesmentioning

confidence: 99%

Adaptive control of Hammerstein–Wiener nonlinear systems

Zhang

Hong

Mao

2014

International Journal of Systems Science

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“…whereθ θ θ k andb k are the estimates of θ θ θ and b respectively. The parameter estimates must be computed such that the system (1) tracks the reference model (2). Now that the goal of the adaptive law is defined, it is possible to proceed with the derivation.…”

Section: B Adaptive Control Of An Input-delay Systemmentioning

confidence: 99%

“…In this section, a scalar system and a multivariable system will be used to demonstrate the performance of the controller. The scalar system example will compare the proposed approach to that in [2].…”

Section: Simulation Examplementioning

confidence: 99%

“…The approach was developed for a scalar system (with a single uncertain parameter) without an uncertain input gain or input time-delay and it was highlighted that extension to more general cases is difficult. In [2], the same problem is addressed without assuming a growth condition on the nonlinearity, in the presence of bounded disturbances. The results are proven for a system similar to that in [1] and the algorithm for multivariable systems is given without any rigorous analysis or stability proofs.…”

Section: Introductionmentioning

confidence: 99%

“…In this paper, a more general implementation inspired by [1] and [2] is presented for uncertain scalar input delay systems with multiple uncertain parameters as well as uncertain input gain. The approach is further extended to multivariable input delay systems.…”

Section: Introductionmentioning

confidence: 99%

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Discrete-Time Adaptive Control for Systems With Input Time-Delay and Non-Sector Bounded Nonlinear Functions

Abidi

Postlethwaite

2019

IEEE Access

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This paper presents a discrete-time adaptive control approach for nonlinear systems with input delay. The nonlinearity is assumed to be non-sector bounded, resulting in the key technical lemma being inapplicable. The main aim of this paper is to present a general implementation inspired from Kanellakopoulos and Fu, et al. for uncertain scalar and multivariable input delay systems with uncertain parameters as well as uncertain input gain. While it has been shown by Kanellakopoulos and Fu, et al. that it is possible to design adaptive control laws that compensate for the growth of the nonlinearity for single parameter scalar systems, a rigorous analysis of multiple parameter systems is not shown. In this paper, it is shown that an adaptive controller design that compensates for the growth of the nonlinearity is possible for both multiple parameter scalar and multivariable systems with input delay. Rigorous stability proofs and simulations are presented to verify the validity of the approach. INDEX TERMS Adaptive control, discrete-time systems, nonlinear control, time-delay systems.

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Robust adaptive control of Hammerstein nonlinear systems and its application to typical CSTR problems

Zhang

Mao

2016

Adaptive Control & Signal

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This paper considers the robust adaptive control of Hammerstein nonlinear systems with uncertain parameters. The control scheme is derived from a modified criterion function which can overcome non-minimum phase property of the linear subsystem. The parameter adaptation is performed by using a robust recursive least squares algorithm with a deadzone weighted factor. The control law compensates the model error by incorporating the unmodeled dynamics estimation. An online pole assignment technique is also presented to guarantee that Assumption 2 always holds. Rigorous theoretical analysis indicates that the parameter estimation convergence and the closed-loop system stability can be guaranteed under mild conditions. Simulation examples including two typical continuous stirred tank reactor problems are studied to verify the effectiveness of the control scheme. ROBUST ADAPTIVE CONTROL OF HAMMERSTEIN NONLINEAR SYSTEMS 165 where f i .u.t // are user-chosen basis functions. This work employs the following polynomial basis functions to approximate the static nonlinearities Figure 2. Adaptive control scheme for Hammerstein system. The initialization is that O Â.0/ D OE1:4; 0:12; 0:8; 0:1; 0:35; 0:7; 0:05; 0:2 T y.0/ D v.0/ D u.0/ D 0, P .0/ D 10 5 I , $ D 0:75, D 0:02 for noise-free case or D 0:1 for noisy case. Simulations are conducted under the following initial conditions: Condition 1 x 3 .0/ D 0:8467; x 4 .0/ D 1:3796; y R .0/ D x 5 .0/ D 1:2737; u Q .0/ D 0 Condition 2. x 3 .0/ D 1; x 4 .0/ D 0:3796; y R .0/ D x 5 .0/ D 0:7737; u Q .0/ D 0

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Robust adaptive regulation of discrete time nonlinear systems with arbitrary nonlinearities

Cited by 8 publications

References 8 publications

Adaptive control of Hammerstein–Wiener nonlinear systems

Adaptive control of Hammerstein–Wiener nonlinear systems

Discrete-Time Adaptive Control for Systems With Input Time-Delay and Non-Sector Bounded Nonlinear Functions

Robust adaptive control of Hammerstein nonlinear systems and its application to typical CSTR problems

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